Abstract

The main purpose of this paper is to analyze the influence on the structure of a finite group of some subgroups lying in the hypercenter. More precisely, we prove the following: Let F be a Baer-local formation. Given a group G and a normal subgroup E of G, let ZF (G) contain a p-subgroup A of E which is maximal being abelian and of exponent dividing pk, where k is some natural number, k = 1 if p = 2 and the Sylow 2-subgroups of E are non-abelian. Then E/ O p (E) ≤ ZF(G/ Op (E)) (Theorem 1). Some well-known results turn out to be consequences of this theorem.